Problem: If $x \dagger y = 8y+3$ and $x \diamond y = 3x-3y$, find $-5 \diamond (-5 \dagger -2)$.
Answer: First, find $-5 \dagger -2$ $ -5 \dagger -2 = (8)(-2)+3$ $ \hphantom{-5 \dagger -2} = -13$ Now, find $-5 \diamond -13$ $ -5 \diamond -13 = (3)(-5)-(3)(-13)$ $ \hphantom{-5 \diamond -13} = 24$.